Thermodynamic conditions for stability in materials with rate-independent dissipation

2005 ◽  
Vol 363 (1836) ◽  
pp. 2479-2515 ◽  
Author(s):  
Henryk Petryk
Keyword(s):  
Standard Condition ◽  
Martensitic Transformations ◽  
Internal Variable ◽  
Irreversible Processes ◽  
Deformation Bands ◽  
Stability Of Equilibrium ◽  
Variable Approach ◽  
Thermodynamic Conditions ◽  
The Stability ◽  
Time Specific

A distinctive feature of the examined class of solids is that a part of the entropy production is due to rate-independent dissipation, as in models of plasticity, damage or martensitic transformations. The standard condition for thermodynamic stability is shown to be too restrictive for such solids and, therefore, an extended condition for stability of equilibrium is developed. The classical thermodynamic theory of irreversible processes is used along with the internal variable approach, with the emphasis on the macroscopic effects of micro-scale instabilities in the presence of two different scales of time. Specific conditions for material stability against internal structural rearrangements under deformation-sensitive loading are derived within the incremental constitutive framework of multi-mode inelasticity. Application to spontaneous formation of deformation bands in a continuum is presented. Conditions for stability or instability of a quasi-static process induced by varying loading are given under additional constitutive postulates of normality and symmetry. As illustration of the theory, the stability of equilibrium or a deformation path under uniaxial tension is analysed for a class of inelastic constitutive laws for a metal crystal deformed plastically by multi-slip or undergoing stress-induced martensitic transformation.

scholarly journals Renovation Management Method in Neglected Buildings

2021 ◽  
Vol 13 (2) ◽  
pp. 929
Author(s):  
Beata Nowogońska ◽  
Magdalena Mielczarek
Keyword(s):  
Decision Making ◽  
Technical Condition ◽  
Irreversible Processes ◽  
Management Method ◽  
The Stability ◽  
Motivating Factor ◽  
Decision Making Support

Renovation works to buildings are often not carried out or there are shifts in time, which causes degradation of the building. The article presents an analysis of the consequences of abandoning renovation works. The aim of this article is to present a method of preliminarily planning renovations of a MRUB (Managing Renovation in Un-renovated Buildings). This method of decision-making support is based on the consequences in the case of the omission of renovations. The omission of renovations may lead to a threat to the stability of the building’s structure, threaten the lives of its users, and further damage the building by damaging further elements, or even cause a building disaster. Often, as a result of the abandonment of renovation, usually caused by the lack of the owner, improper manager, or irresponsible owners, these objects are degraded. The consequences of the failure of renovating buildings lead to irreversible processes of destruction. As a result of the research, it was found that it was not only a bad technical condition that was a prerequisite for carrying out the renovation. The consequences of the absence of renovation works, in addition to the technical condition, should be a motivating factor. The problem of the abandonment of renovations is presented using the example of the palace in Drwalewice.

scholarly journals Numerical Exploration of Kaldorian Interregional Macrodynamics: Enhanced Stability and Predominance of Period Doubling under Flexible Exchange Rates

2010 ◽  
Vol 2010 ◽  
pp. 1-29 ◽  
Author(s):  
Toichiro Asada ◽  
Christos Douskos ◽  
Vassilis Kalantonis ◽  
Panagiotis Markellos
Keyword(s):  
Exchange Rates ◽  
Government Expenditure ◽  
Period Doubling ◽  
Numerical Approach ◽  
Capital Movement ◽  
Dimensional Parameter ◽  
Stability Of Equilibrium ◽  
The Stability ◽  
Flexible Exchange Rates ◽  
Enhanced Stability

We present a discrete two-regional Kaldorian macrodynamic model with flexible exchange rates and explore numerically the stability of equilibrium and the possibility of generation of business cycles. We use a grid search method in two-dimensional parameter subspaces, and coefficient criteria for the flip and Hopf bifurcation curves, to determine the stability region and its boundary curves in several parameter ranges. The model is characterized by enhanced stability of equilibrium, while its predominant asymptotic behavior when equilibrium is unstable is period doubling. Cycles are scarce and short-lived in parameter space, occurring at large values of the degree of capital movementβ. By contrast to the corresponding fixed exchange rates system, for cycles to occur sufficient amount of trade is requiredtogetherwith high levels of capital movement. Rapid changes in exchange rate expectations and decreased government expenditure are factors contributing to the creation of interregional cycles. Examples of bifurcation and Lyapunov exponent diagrams illustrating period doubling or cycles, and their development into chaotic attractors, are given. The paper illustrates the feasibility and effectiveness of the numerical approach for dynamical systems of moderately high dimensionality and several parameters.

scholarly journals Low-temperature triple-capillary cryostat for ice crystal growth studies

2019 ◽  
Vol 12 (11) ◽  
pp. 6143-6152 ◽  
Author(s):  
Brian D. Swanson ◽  
Jon Nelson
Keyword(s):  
Radiative Properties ◽  
Growth Chamber ◽  
Thermal Mass ◽  
Ice Crystal ◽  
Vapor Source ◽  
Crystal Forms ◽  
New Instrument ◽  
Crystal Substrate ◽  
Thermodynamic Conditions ◽  
The Stability

Abstract. Ice crystals come in a remarkable variety of shapes and sizes that affect a cloud's radiative properties. To better understand the growth of these crystals, we built an improved capillary cryostat (CC2) designed to reduce potential instrumental artifacts that may have influenced earlier measurements. In CC2, a crystal forms at the end of one, two, or three well-separated, ultrafine capillaries to minimize both potential crystal–crystal and crystal–substrate interaction effects. The crystals can be initiated using several ice-nucleation modes. The cryostat has two vapor-source chambers on either side of the growth chamber, each allowing independent control of the growth chamber supersaturation. Crystals can be grown under a range of air pressures, and the supersaturation conditions in the growth chamber can be rapidly changed by switching between the two vapor-source chambers using a sliding valve. Crystals grow fixed to the capillary in a uniform, stagnant environment, and their orientation can be manipulated to measure the growth rate of each face. The high thermal mass of CC2 increases the stability and uniformity of the thermodynamic conditions surrounding the crystals. Here we describe the new instrument and present several sample observations.

Sign in / Sign up

Export Citation Format

Share Document